The invention relates to a method and an arrangement for computing values s.sub.i (x.sub.0 +.DELTA.x,y.sub.0 +.DELTA.y) of pixels which are arranged outside a two-dimensional scanning raster {x.sub.0 .+-.n, y.sub.0 .+-.m, with m,n=0,1,2,3, . . . } of pixels having pixel values s(x.sub.0 .+-.n,y.sub.0 .+-.m) of a digital picture signal.
In such methods and arrangements for computing new pixel values, it is important to determine the values of pixels which are located outside a two-dimensional scanning raster. The known pixels are situated at locations (x.sub.0 .+-.n,y.sub.0 .+-.m) in which m and n are integers of zero up to a maximal value. The pixels of a digital picture signal which are located in this scanning raster have known pixel values. By way of non-limitative example, it is herein assumed that the distance between two adjacent pixels is 1 in the horizontal and vertical directions.
For example, for the purpose of television signal conversion, conversion between different graphic modes in PCs, video data compression, or for medical applications, it is often desirable or necessary to determine pixel values of pixels which are not located at the predetermined points on the two-dimensional scanning raster but are located between these points. Fundamentally, the searched pixel values may have arbitrary positions between the points on the scanning raster. This complicates their computation.
In the state of the art, methods are known which are based on bilinear or bicubic interpolation for computing such new pixel values in their simplest case. In bilinear interpolation, a linear weighting of the four pixels located closest to a searched pixel in the scanning raster is performed. In the interpolation by means of cubic B-splines, an ideal interpolation filter is approximated by means of a sin(x)/x-shaped pulse response for the one-dimensional case by means of a 3rd-order polynomial, which minimizes the interpolation error, but strongly reduces the resolution. Cf. K. Pratt: "Digital Image Processing", second edition, pp. 114 etc.
For computing new pixel values, it is further possible to perform a combined up and down-sampling.
EP-A-660 514 discloses a filter which operates as a one-dimensional polynomial interpolator and in which a one-dimensional polynomial is set up which should approximate the pixel values located outside a one-dimensional scanning raster as satisfactorily as possible.